The heat energy that must be supplied to 14 gram of nitrogen at room temperature to raise its temperature by 48^ C at constant pressure is (Molecular weight of nitrogen =28, R= gas constant, C_p= 7 2 R for diatomic gas)

Step-by-step solution

Heat energy supplied at constant pressure is governed by Q_p = n C_p T , where n is the number of moles, C_p is molar specific heat at constant pressure, and T is the temperature change. For diatomic nitrogen, molar specific heat at constant pressure is C_p = 7 2 R . Given a mass of 14 g and molecular weight 28 g/mol, the number of moles is n = 14 28 = 0.5 mol. With T = 48^ C : Q_p = (0.5) ( 7 2 R ) 48 = 0.5 7 2 48 R = 7 4 48 R = 7 12 R = 84 R . The result is 84 R , which corresponds to option B .